Practice Function Tables and Graphs in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

A function table (input-output table) lists paired values of a function, and its graph is the visual representation of those pairs as points on the coordinate plane.

A function is like a machine: put a number in, get a number out. The table records what goes in and comes out, and the graph draws the picture.

Showing a random 20 of 50 problems.

Example 1

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A table for ff: x:1,2,3x:1,2,3, f(x):2,4,8f(x):2,4,8. Predict f(4)f(4) assuming the pattern continues.

Example 2

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Which input gives output 0 for y=2x−6y = 2x - 6 (use a table idea)?

Example 3

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A table shows x:0,1,2x:0,1,2 and y:5,8,11y:5,8,11. What is the yy-intercept of its graph?

Example 4

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A table has x:0,1,2,3x:0,1,2,3 and y:0,2,4,6y:0,2,4,6. Write the function rule.

Example 5

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A line on a graph rises 2 for every 1 right and hits (0,1)(0,1). Write its equation.

Example 6

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In a table, which column is usually the input?

Example 7

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yy varies linearly with xx. y=2y=2 when x=1x=1 and y=8y=8 when x=4x=4. Find yy when x=10x=10.

Example 8

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A graph of y=mx+by=mx+b passes through (1,7)(1,7) and (4,1)(4,1). Find mm and bb.

Example 9

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Table: x:0,1,2,3x:0,1,2,3, y:3,6,11,18y:3,6,11,18. Is it linear? Justify by looking at first and second differences.

Example 10

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A table of perimeter PP vs side ss for a square: s:1,2,3s:1,2,3, P:4,8,12P:4,8,12. Find the rule.

Example 11

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Why is the vertical line test valid for identifying functions from graphs?

Example 12

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A table represents a discrete function: pages read per day. Why might it NOT make sense to connect the dots on its graph?

Example 13

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Two tables: A has y=3xy=3x; B has y=x+6y=x+6. Which input makes them agree?

Example 14

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f(x)=2x+1f(x)=2x+1 and g(x)=3x−4g(x)=3x-4. For what xx does f(x)=g(x)f(x)=g(x)?

Example 15

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The graph of y=2xy=2x — does it pass through the origin?

Example 16

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A graph is a straight line. What family of function is it?

Example 17

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From y=4xy = 4x, complete the row for x=5x = 5.

Example 18

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Two graphs: y=2xy=2x and y=x+3y=x+3. At what point do they meet?

Example 19

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A table shows x:1,2,3x:1,2,3, y:4,7,10y:4,7,10. Find the rule.

Example 20

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A graph shows points (1,2),(2,4),(3,6)(1,2),(2,4),(3,6). Are they on one line through the origin?
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